to cause a persuasive movement in any large body of influence, i.e., a mass of people, through means by which a lesser influence is utilized.

From the phrase, 'It's the tail that wags the dog.' This can be seen when a dog begins to wag it's tail, and it's body then follows.

in partisan politics, an unpopular party will wag the dog using a variety of provocative political manoeverings and machinations to undermine the public favour from the popular party, out of which a momentum can be borne.

To cause a desired result by means other than the obvious or rational method. Imagine you want a dog to wag it's tail. You should make the dog happy, and the tail will wag. If you can't or won't make the dog happy, you can get the tail to wag by "wagging the dog".

When the college saw that black students were failing Calculus at a disproportionately high rate to their enrollment, they decided to wag the dog by making the tests less difficult.

To start a war or military operation to divert negative politcal attention away from yourself. Based on the movie of the same name, where the President fabricates a fake war to take political pressure away from a scandal.

When Cater ordered Opertaion Eagle Claw he was playing wag the dog, because he was a very unpopular and weak President and wanted to seem like he handled it strongly.

It is suggested that Clinton wagged the dog by helping NATO bomb Kosovo at the same time as the Lewinski scandal. This theory came about because the film had just been released.